The age of father is twice that of elder son. Ten years hence, the age of the father will be three times that of the younger son. If the difference of ages of the two sons is $15$ years, find the age of the father.

Let the current age of the father be $F$, elder son be $E$, and younger son be $Y$.
From the problem, we have:

1. $F=2E⟹E=\frac{F}{2}$
2. $F+10=3(Y+10)⟹F+10=3Y+30⟹3Y=F-20⟹Y=\frac{F-20}{3}$
3. The difference between the ages of the two sons is $15$ years:

$$E-Y=15$$

Substitute the values of $E$ and $Y$ in terms of $F$:

$$\frac{F}{2}-\frac{F-20}{3}=15$$

Taking LCM of 2 and 3, which is 6:

$$\frac{3F-2(F-20)}{6}=15$$

$$3F-2F+40=15\times 6$$

$$F+40=90$$

$$F=50$$

Thus, the age of the father is $50$ years.